Seminar Details

Date

5-12-2003

Time

9:30

Room/Location

218

Title

Denotational semantics for View-based Database Mappings

Speaker

Zoran Majkic

Affiliation

Univ. di Roma

Link

Abstract

This document presents a categorical denotational semantics for
database mapping, based on views, in the most general framework,
database-integration/exchange and Peer-to-peer. The base database
category DB (instead of traditional Set category) , with objects
database-instances and with morphisms (mappings which are not
functions) between them, is used (at instance level) as a proper
semantic domain for a database mappings based on a set of complex
query computations. The higher (logical) level schema mappings
between databases, usually written in some high expressive logical
language (for example, LAV, GAV, GLAV, tuple generating dependency)
may be functorially translated into this base "computation" category.
The new approach based on the behavioral point of view for databases
is assumed, and are established behavioural equivalences for databases
and their mappings. The introduction of observations, which are
computations without side-effects, also defines the fundamental (from
Universal algebra) monad endofunctor T, which is also the closure
operator for objects and for morphisms such that the database lattice
is an algebraic (complete and compact) lattice,
where Ob{DB} is a set of all objects (database instances) of DB
category and "\preceq" is a preorder relation between them. The join
and meet operators of this database lattice are Merging and Matching
database operators respectively. The resulting 2-category DB is
symmetric (also a mapping is represented as an object, that is, a
database instance), so, a mappings between mappings are a 1-cell
morphisms for all higher meta-theories: each mapping is a homomorphism
from a Kleisli monadic T-coalgebra into the cofree monadic
T-coalgebra. The database category DB has nice properties: it is
equal to its dual, complete and cocomplete, locally small and locally
finitely presentable, and monoidal biclosed V-category enriched over
itself. The monad derived from the endofunctor T is an enriched monad.
Generally, database mappings are not simply programs from values
(relations) into computations (views) but an equivalence of
computations: because of that each mapping, from any two databases A
and B, is equivalently reversible and gives a duality property to the
category DB. The denotational semantics of database mappings is given
by morphisms of the Kleisli category DB_T which may be "internalized"
in DB category as "computations". Special attention is devoted to
some practical examples: query definition, query rewriting in the
Database-integration environment, P2P mappings and their equivalent
GAV translation.